There are no sharply transitive subsets of $\mathrm{SL}(2,q)$ for $q\ge 13$

John Bamberg, Sam Mattheus

It was known at least to L.E. Dickson in 1901 that $\mathrm{SL}(2,q)$, in its natural action on ${\mathbb{F}}_q^2\setminus \{0\}$, has a sharply transitive subgroup only when $q\in\{2…